So I originally had a power outage when moving a partition and that is why I was using TestDisk now. The partition had taken around 8 days and was almost done. I have since been running TestDisk for the past several days, maybe 7 or 8 also. I am not sure how close to being done, but it did recover many files.

But the power just went out again... So I am wondering what to do now? Can I somehow pick up where TestDisk left off when recovering my files? If so, how?

If you were running PhotoRec, you can restart it and choose to resume the recovery.

I was just using the normal TestDisk, I first analyzed the data. And then was copying the found files over to the hard drive. But the power went out after around 6000 files were recovered, but still was not completely done.